Electromagnetic waves differ from mechanical waves mainly because it does not need a medium for the waves to pass through.In electromagnetic wave theory, light is composed of electric and magnetic fields in which these fields are perpendicular to each other, thus they are transverse waves.
All electromagnetic waves move at the speed of light measured in a vacuum.As experimental techniques improved during the past centuries, the accuracy and precision for the speed of light was greatly increased.The exact speed of light traveling in a vacuum is 299,792,458 m/s but 3.00 X 10^8 is precise enough to be used.In this chapter, the speed of light in a vaccum will be represented by c, therefore the equation for the all electromagnetic waves speed is
Physicist Christian Huygens, who derived the Huygens’ principle for all waves, stated that all of the points on a wave front can be considered as point sources that will create a circular or spherical wavelet.These wavelets will then constructively interfere on a tangent line to the fronts of them, which would result in new wave fronts.
14-2 Flat Mirrors
Reflection of light on a given surface is the change in the direction of light and reflects the rest.How light is reflected depends on the surface texture, where diffuse reflection is light being reflect off a rough surface in comparison to specular reflection, light feflected from smooth surfaces, such as a mirror.
The symmetry of reflected light is described by the law of reflection, which states that the angles of the incoming and reflected rays are equal.Therefore, the angle of incidence is in direct propotion to the angle of reflection.
The flat mirror is considered the simplest form of all mirrors.An object can be placed at a distance in front of the flat mirror, the light bounces off the object and is then reflected from the smooth and shinny surface of the mirror.Specific rays of are created after the collision of light and always come from behind the mirror.Since the final positions of the rays are on the other side, the image formed by these rays is a virtual image.The object’s distance and image distance, represented by p and q, will always be equal in a flat mirror.The same applies to the height of the object and the resulting image.
Ray diagrams are useful to determine the final position of an object’s image.Picture of flat mirror ray diagram.
4-3 Curved Mirrors
There are two types of curved mirrors, which are concave (curving inward in the middle) and convex (curving outward).These parabolic mirrors can be compared to a section of a sphere with the racius of curvature R, a focal length that is measured from the distance from the center of the mirror to its focal point F.More importantly, the focal point is half the distance of the radius of curvature.In curved mirrors, p and q are positive if they are measured to a specific point in front of the mirror and negative if behind.
The relationship between focal length, object distance, and image distance is:
Also the ratio of an object’s initial height and final height is the magnification, M, and is:
When drawing a ray diagram, consider these general rules:
A ray that comes in parallel to the principal axis goes out through the focal point
2. A ray that comes in through the focal point and goes out parallel to the principal axis.
3. A ray that goes in through the center of curvature reflects perpendicular off the miorror, and goes back out along the same line where it came in.
Examples:
A concave spherical mirror has a focal length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the image.
Given: f=+10.0 cm p=+30.0 cm
The mirror is concave, so f is positive. The object is in front so p is positive.
Use the equation:
14-3 Color and Polarizations
Colors are composed of both primary colors (red, green, blue or RGB) and primary colors of pigments which are cyan, magenta, and yellow (used in printers today).When all primary colors are mixed, black is then formed.Primary colors for additive mixing are the secondary colors for subtractive mixing.
A beam of light can however, be polarized or filtered more than once if there consists of various material, so the intensity of the light will be proportional to the cosine of the angle between the polarizing filters.
Electromagnetic waves differ from mechanical waves mainly because it does not need a medium for the waves to pass through. In electromagnetic wave theory, light is composed of electric and magnetic fields in which these fields are perpendicular to each other, thus they are transverse waves.
All electromagnetic waves move at the speed of light measured in a vacuum. As experimental techniques improved during the past centuries, the accuracy and precision for the speed of light was greatly increased. The exact speed of light traveling in a vacuum is 299,792,458 m/s but 3.00 X 10^8 is precise enough to be used. In this chapter, the speed of light in a vaccum will be represented by c, therefore the equation for the all electromagnetic waves speed is
Physicist Christian Huygens, who derived the Huygens’ principle for all waves, stated that all of the points on a wave front can be considered as point sources that will create a circular or spherical wavelet. These wavelets will then constructively interfere on a tangent line to the fronts of them, which would result in new wave fronts.
14-2 Flat Mirrors
Reflection of light on a given surface is the change in the direction of light and reflects the rest. How light is reflected depends on the surface texture, where diffuse reflection is light being reflect off a rough surface in comparison to specular reflection, light feflected from smooth surfaces, such as a mirror.
The symmetry of reflected light is described by the law of reflection, which states that the angles of the incoming and reflected rays are equal. Therefore, the angle of incidence is in direct propotion to the angle of reflection.
The flat mirror is considered the simplest form of all mirrors. An object can be placed at a distance in front of the flat mirror, the light bounces off the object and is then reflected from the smooth and shinny surface of the mirror. Specific rays of are created after the collision of light and always come from behind the mirror. Since the final positions of the rays are on the other side, the image formed by these rays is a virtual image. The object’s distance and image distance, represented by p and q, will always be equal in a flat mirror. The same applies to the height of the object and the resulting image.
Ray diagrams are useful to determine the final position of an object’s image. Picture of flat mirror ray diagram.
4-3 Curved Mirrors
There are two types of curved mirrors, which are concave (curving inward in the middle) and convex (curving outward). These parabolic mirrors can be compared to a section of a sphere with the racius of curvature R, a focal length that is measured from the distance from the center of the mirror to its focal point F. More importantly, the focal point is half the distance of the radius of curvature. In curved mirrors, p and q are positive if they are measured to a specific point in front of the mirror and negative if behind.
The relationship between focal length, object distance, and image distance is:
Also the ratio of an object’s initial height and final height is the magnification, M, and is:
When drawing a ray diagram, consider these general rules:
- A ray that comes in parallel to the principal axis goes out through the focal point
- 2. A ray that comes in through the focal point and goes out parallel to the principal axis.
- 3. A ray that goes in through the center of curvature reflects perpendicular off the miorror, and goes back out along the same line where it came in.
Examples:A concave spherical mirror has a focal length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the image.
Given: f=+10.0 cm p=+30.0 cm
The mirror is concave, so f is positive. The object is in front so p is positive.
Use the equation:
14-3 Color and Polarizations
Colors are composed of both primary colors (red, green, blue or RGB) and primary colors of pigments which are cyan, magenta, and yellow (used in printers today). When all primary colors are mixed, black is then formed. Primary colors for additive mixing are the secondary colors for subtractive mixing.
A beam of light can however, be polarized or filtered more than once if there consists of various material, so the intensity of the light will be proportional to the cosine of the angle between the polarizing filters.
Sources:
Faughn, Jerry S. and Raymond A. Serway. Physics. New York: Holt, 2004.
Strong, Tom. Course notes. Honors Physics, Dept. of Science, Mount Lebanon High School. 2009.
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